Pay particular attention to patterns. If you've been doing the above step, hopefully you noticed that there are several parts of words that are the same. There are groups of words, for instance, which end in "-ology" or "-logy". This is called a suffix, it goes at the end of the word. "-logy" means "study", so any word ending in -logy will mean "The study of _____". Geo- means "ground", so "Geology" is "The study of the ground/rocks." Geo- is a prefix, which is like a suffix, except that it goes onto the beginning of words. You could make lists of these patterns, and wherever you see them, write down words that have that prefix or suffix, and find out what they mean.
Get to know your prefixes. Prefixes are as important as suffixes in finding out what a word means. Here is just a small list, many of which you'll recognise: Super, Hypo, Hyper, Under, Over, De, Dis, Un, A/an. This website provides a comprehensive list of prefixes vocabulary. If you can identify a prefix then you can already partly tell what the word represents. If a word has the prefix "un" or "non", then you know that the word will mean that something is not doing something, or something isn't something. Unnoticed means "not noticed", a non-smoker is someone who does not smoke.
Learn another language. It sounds bizarre, but learning another language may help you to better understand your own. Learning how to analyse and take apart a language will allow you to analyse and take apart individual words. In particular, learning Latin or Greek will open up a lot of English to you as most of it is based off of those two languages. In fact, many Latin words have been nicked by English, unchanged. Memorandum, referendum, ad hoc, bona fide, pro bono, in vitro, re, vice versa, et cetera...
Test this wherever you go. Look at an unfamiliar word, and break it down into roots. Antidisestablishmentarianism might sound ghastly, and indeed it is, until you break it down. There's actually only one word in there, the rest are prefixes and suffixes. It can be split into Anti, dis, establish, ment, arian, ism. To establish something means to set something up. -ment is a suffix that turns a verb, or a doing word, into a noun. Establishment is the doing of that action. Dis means "not" or "the opposite of" and so Disestablishment is the opposite of Establishment. To Disestablish something is to break it up. -arian means "believer in" or "follower of." So a Disestablishmentarian is someone who believes that we should disestablish things. And "ism" is the suffix given to a practice or belief (such as Judaism or Hinduism,) so Disestablishmentarianism is the belief that we should break apart something. And Anti- means "against". So Antidisestablishmentarianism is the opposition to Disestablishmentarianism! In the case of this word, the disestablishment refers to separation of church and state, in case you were interested. But don't worry about words like that because most words aren't nearly that long! (Well, there's always pneumonoultramicroscopicsilicovolcanoconiosis, and that's just a lung disease!)
- Keep a notebook. This could be useful if you come across a word that you want to learn later, if you want to list any words that share suffixes or prefixes (both of which are known as "roots", which also include anything that goes into the middle.)
- Own a dictionary. It's somewhat counter-intuitive (counter meaning opposite, and intuitive meaning an idea, so counter-intuitive would mean "opposing the idea") to tell you this, but really, until you learn more about etymology, a dictionary is a useful aid!
- Read etymology dictionaries. They are found online and presumably in bookstores if you look hard enough. Learning about the origins of words will really help you to understand other words.